Efficient one-sided linearization of spline geometry

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2768, Issue , 2003, Pages 297-319

  Peters, Jörg ^a  

^a J Crayton Pruitt Family Department of Biomedical Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; LINEARIZATION;

COMPUTATIONALLY EFFICIENT; ERROR BOUND; FORBIDDEN REGION; GEOMETRY REPRESENTATION; MAX-NORMS; PAPER SURVEYS; POLYTOPES; SPLINE SURFACES;

COMPUTATIONAL GEOMETRY;

EID: 21144446096     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-39422-8_20     Document Type: Article

References (30)

1. Pankaj K. Agarwal and Subhash Suri. Surface approximation and geometric partitions. SIAM Journal on Computing, 27(4):1016-1035, August 1998.
2. Julien Basch. Kinetic Data Structures. PhD thesis, Stanford University, 1999.
3. R. C. Buck. Applications of duality in approximation theory. In Approximation of Functions (Proc. Sympos. General Motors Res. Lab., 1964), pages 27-42. Elsevier Publ. Co., Amsterdam, 1965.
4. Jonathan Cohen, Amitabh Varshney, Dinesh Manocha, Greg Turk, Hans Weber, Pankaj Agarwal, Frederick P. Brooks, Jr., and William Wright. Simplification envelopes. In Holly Rushmeier, editor, SIGGRAPH 96 Conference Proceedings, Annual Conference Series, pages 119-128. ACM SIGGRAPH, Addison Wesley, August 1996. held in New Orleans, Louisiana, 04-09 August 1996.
5. A. Crosnier and J. R. Rossignac. Technical section - tribox bounds for three-dimensional objects. Computers and Graphics, 23(3):429-437, June 1999.
6. Joe Czyzyk, Sanjay Mehrotra, Michael Wagner, and Stephen Wright. http://www-fp.mcs.anl.gov/otc/Tools/PCx.
7. D. Dobkin, E.R. Gansner, E. Koutsofios, and S.C. North. A path router for graph drawing. In Proceedings of the 14th annual symposium on Computational Geometry, pages 415-416. ACM Press, New York, 1998. June 1-10 1998, Minneapolis, MN.
8. Gerald Farin. Tighter convex hulls for rational Bézier curves. Comput. Aided Geom. Design, 10:123-125, 1993.
9. Daniel Filip, Robert Magedson, and Robert Markot. Surface algorithms using bounds on derivatives. CAGD, 3(4):295-311, 1986.
10. S. Gottschalk, M. C. Lin, and D. Manocha. OBBTree: A hierarchical structure for rapid interference detection. Computer Graphics, 30(Annual Conference Series):171-180, 1996.
11. Timothy L. Kay and James T. Kajiya. Ray tracing complex scenes. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 269-278, August 1986.
12. James T. Klosowski, Joseph S. B. Mitchell, Henry Sowizral, and Karel Zikan. Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs. IEEE Transactions on Visualization and Computer Graphics, 4(1):21-36, January 1998.
13. James Thomas Klosowski. Efficient collision detection for interactive 3d graphics and virtual environments. PhD thesis, State Univ. of New York at Stony Brook, May 1998.
14. Leif P. Kobbelt, Katja Daubert, and Hans-Peter Seidel. Ray tracing of subdivision surfaces. In Rendering Techniques '98 (Proceedings of the Eurographics Workshop), pages 69-80, New York, June 1998. Springer-Verlag.
15. D. Lutterkort and J. Peters. Smooth paths in a polygonal channel. In Proceedings of the 15th annual symposium on Computational Geometry, pages 316-321, 1999.
16. D. Lutterkort and J. Peters. Optimized refinable enclosures of multivariate polynomial pieces. Comput. Aided Geom. Design, 18(9):851-863, 2001.
17. David Lutterkort. Envelopes for Nonlinear Geometry. PhD thesis, Purdue University, May 2000.
18. D. Nairn, J. Peters, and D. Lutterkort. Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon. Computer Aided Geometric Design, 16(7):613-633, Aug 1999.
19. N. M. Patrikalakis and T. Maekawa. Shape Interrogation for Computer Aided Design and Manufacturing. Springer-Verlag, Berlin, 2002.
20. N.M. Patrikalakis and T. Maekawa. Intersection problems. In Handbook of Computer Aided Geometric Design. Springer, 2001.
21. J. Peters and X. Wu. On the optimality of piecewise linear max-norm enclosures based on slefes. In Proceedings of the 2002 St Malo conference on Curves and Surfaces, 2003.
22. Jörg Peters and Xiaobin Wu. Optimized refinable surface enclosures. Technical report, University of Florida, 2000.
23. Jörg Peters and Xiaobin Wu. Sanwiching spline surfaces. Computer-Aided Geometric Design, 200x.
24. 1-approximation. Cambridge University Press, Cambridge, 1989.
25. U. Reif. Best bounds on the approximation of polynomials and splines by their control structure. Comput. Aided Geom. Design, 17(6):579-589, 2000.
26. P.V. Sander, Xianfeng Gu, S.J. Gortler, H. Hoppe, and J. Snyder. Silhouette clipping. Computer Graphics, 34(Annual Conference Series):327-334, 2000.
27. T. W. Sederberg and R. T. Farouki. Approximation by interval bezier curves. IEEE Computer Graphics and Applications, 12(5):87-95, September 1992.
28. Thomas W. Sederberg, Scott C. White, and Alan K. Zundel. Fat arcs: A bounding region with cubic convergence. Comput. Aided Geom. Design, 6:205-218, 1989.
29. G. Shen and N.M. Patrikalakis. Numerical and geometric properties of interval B-splines. International Journal of Shape Modeling, 4(1,2):35-62, 1998.
30. E. Welzl. Smallest enclosing disks (balls and ellipsoids). In Hermann Maurer, editor, Proceedings of New Results and New Trends in Computer Science, volume 555 of LNCS, pages 359-370, Berlin, Germany, June 1991. Springer.